Efficient computation of lattice Green's functions for models with nearest-neighbour hopping
Bibliographic record
Abstract
We show that for models with nearest-neighbour (nn) hopping, the lattice Green's functions can be calculated without the need to perform integrals. Our method applies to rectangular, triangular and honeycomb lattices in two dimensions, and to simple, face-centered and body-centered lattices in three dimensions. External magnetic fields can be dealt with trivially. As an example, we show that our method works for any ratio ϕ/ϕ 0 of the magnetic flux through the unit cell, i.e. irrespective of the change in the size of the magnetic unit cell. Other straightforward generalizations are to models with multiple orbitals per site, with any spin-orbit coupling, on-site disorder, and any combinations thereof. The method works equally well in the presence of surfaces. In all cases, accurate values for large distances can be obtained very efficiently and without finite-size effects. The relationship to other computational methods is also analyzed.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".